Is w + h^4 positive?

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

jjjinapinch: Senior | Next Rank: 100 Posts; Posts: 83; Joined: Mon Jul 24, 2017 8:16 am; Followed by:1 members

Is w + h^4 positive?

by jjjinapinch » Thu Jul 27, 2017 12:12 pm

Is w + h^4 positive?

(1) h is positive
(2) w is positive

Official Guide question
Answer: B

Quote

Source: Beat The GMAT — Data Sufficiency | Thu Jul 27, 2017 12:12 pm

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Thu Jul 27, 2017 12:34 pm

jjjinapinch wrote:Is w + h^4 positive?
(1) h is positive
(2) w is positive

Official Guide question
Answer: B

Target question: Is w + h^4 positive?

Statement 1: h is positive
Let's TEST some values.
There are several values of w and h that satisfy statement 1. Here are two:
Case a: w = 1 and h = 1. In this case, w + h^4 = 1 + 1^4 = 2. So, w + h^4 IS positive
Case b: w = -3 and h = 1. In this case, w + h^4 = -3 + 1^4 = -2. So, w + h^4 is NOT positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: w is positive
Important concept: (any number)^(even integer) = a value greater than or equal to 0
Statement 2 tells us that w is some positive number
We can write: w + h^4 = (some positive number) + ( a value greater than or equal to 0)
We can see that w + h^4 positive is definitely positive
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Quote

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Thu Jul 27, 2017 12:38 pm

Hi jjjinapinch,

This question is built around some Number Property Rules, so you can either TEST VALUES or use those NP rules to get to the correct answer.

We're asked if (W + H^4) is positive. This is a YES/NO question.

Before we get to the two Facts, it's worth noting that H^4 can NEVER be negative (it can be 0 when H=0, but in all other situations, H^4 will be POSITIVE). Thus, this question really comes down to the value of W....

1) H is positive

Fact 1 tells us that H is POSITIVE, so H^4 will be POSITIVE. However, it does NOT tell us anything about the value of W.

IF... H=1, W=1, then (H+W^4) = 2 and the answer to the question is YES.
IF... H=1, W= -2, then (H+W^4) = -1 and the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) W is positive

Since W is POSITIVE, and we know that H^4 is >= to 0, then we know that (W+H^4) MUST be POSITIVE and the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Quote

GMAT/MBA Expert

Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Thu Jul 27, 2017 10:40 pm

jjjinapinch wrote:Is w + h^4 positive?

(1) h is positive
(2) w is positive

Official Guide question
Answer: B

We need to ensure whether (w + h^4) positive.

Since the exponent of h is 4, an even number, whether h is positive or negative, h^4 is positive.

Thus, (w + h^4) is positive, if

1. w is positive, or
2. w is negative, but |w| < h^4

(w + h^4) is NOT positive, if

w is negative, and |w| â‰¥ h^4

Statement 1: h is positive.

We already know the nature of h^4, we are not interested in the nature of h. Insufficient.

Statement 2: w is positive.

We already deduced that if w is positive, (w + h^4) is positive. Sufficient.

The correct answer: B

Hope this helps!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Singapore | Doha | Lausanne | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Dec 08, 2017 7:05 am

jjjinapinch wrote:Is w + h^4 positive?

(1) h is positive
(2) w is positive

We need to determine whether w+h^4 is positive. First, we know that h^4 is always non-negative.

Let's look at the 2 possibilities for the value of w+h^4:

1) If w is positive, then (w + h^4) will be positive.

2) If w is negative, then h^4 must be greater than |w| in order for (w + h^4) to be positive. For example if w = -4, then h^4 must be greater than 4 in order for (w + h^4) to be positive.

Statement One Alone:

h is positive

Since we already know that h^4 is positive and do not have any information about w, we do not have enough information to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

w is positive

Since we know that h^4 is non-negative, also knowing that w is positive is enough information to determine that w + h^4 is positive. Statement two is sufficient to answer the question.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]